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Studia Mathematica

2003 | 155 | 1 | 1-21
Tytuł artykułu

The Maurey extension property for Banach spaces with the Gordon-Lewis property and related structures

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The main result of this paper states that if a Banach space X has the property that every bounded operator from an arbitrary subspace of X into an arbitrary Banach space of cotype 2 extends to a bounded operator on X, then every operator from X to an L₁-space factors through a Hilbert space, or equivalently $B(ℓ_{∞},X*) = Π₂(ℓ_{∞},X*)$. If in addition X has the Gaussian average property, then it is of type 2. This implies that the same conclusion holds if X has the Gordon-Lewis property (in particular X could be a Banach lattice) or if X is isomorphic to a subspace of a Banach lattice of finite cotype, thus solving the Maurey extension problem for these classes of spaces. The paper also contains a detailed study of the property of extending operators with values in $ℓ_{p}$-spaces, 1 ≤ p < ∞.
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Tom
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1-21
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wydano
2003
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• Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.
autor
• Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
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